Simultaneous core partitions with nontrivial common divisor

Gramain, Jean Baptiste; Nath, Rishi; Sellers, James A.

doi:10.1007/s11139-020-00289-4

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Extension To the Non-coprime Case1

Introduction1

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2022

2023

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Cited by 3 publications

(2 citation statements)

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“…The structure of (s, t)-core partitions when gcd(s, t) > 1 is substantially different from the coprime case (see, e.g., [6]). In particular, the poset P is infinite and has connected components for each residue classes modulo gcd(s, t).…”

Section: Extension To the Non-coprime Casementioning

confidence: 99%

The Maximum Hook Length of $d$-Distinct Simultaneous Core Partitions

Pesikoff,

Przybocki,

Xia

2023

Electron. J. Combin.

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Section: Extension To the Non-coprime Casementioning

confidence: 99%

The Maximum Hook Length of $d$-Distinct Simultaneous Core Partitions

Pesikoff,

Przybocki,

Xia

2023

Electron. J. Combin.

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“…Additionally, we hire a well-known object so called self-conjugate core partitions to enumerate the number of such core partitions. For instance, bar-core partitions and self-conjugate core partitions are related to each other; Yang [14,Theorem 1.1] constructed a bijection between the set of self-conjugate s-cores and that of s-cores for odd s; Gramain, Nath, and Sellers [8,Theorem 4.12] gave a bijection between self-conjugate (s, t)-core partitions and (s, t)-core partitions, where both s and t are coprime and odd.…”

Section: Introductionmentioning

confidence: 99%

Results on bar-core partitions, core shifted Young diagrams, and doubled distinct cores

Cho¹,

Nam²,

Sohn³

2022

Preprint

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Simultaneous bar-cores, core shifted Young diagrams (or CSYDs), and doubled distinct cores have been studied since Morris and Yaseen introduced the concept of bar-cores. In this paper, our goal is to give a formula for the number of these core partitions on (s, t)-cores and (s, s + d, s + 2d)-cores for the remaining cases that are not covered yet. In order to achieve this goal, we observe a characterization of s-core partitions to obtain characterizations of doubled distinct s-core partitions and s-CSYDs. By using them, we construct N E lattice path interpretations of these core partitions on (s, t)-cores. Also, we give free Motzkin path interpretations of these core partitions on (s, s + d, s + 2d)-cores.

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